Question

If both (x – 2) and (x – 1/2) are factors of px² + 5x + q, show that p = q.

Answer 1

Let f(x) = px² + 5x + q, if (x – 2) is the factor of f(x)

from (1) and (2) 

⇒ 4p + 10 + q = p + 10 + 4q

⇒ 4p + q = p + 4q 

⇒ 4p – p = 4q – q 

⇒ 3p = 3q 

⇒ p = q